Question: Simplify the following expression: $ r = \dfrac{-9t}{6t + 5} + 4 $
In order to subtract expressions, they must have a common denominator. Multiply the second expression by $\dfrac{6t + 5}{6t + 5}$ $ \dfrac{-4}{1} \times \dfrac{6t + 5}{6t + 5} = \dfrac{-24t - 20}{6t + 5} $ Therefore $ r = \dfrac{-9t}{6t + 5} - \dfrac{-24t - 20}{6t + 5} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{-9t - (-24t - 20) }{6t + 5} $ Distribute the negative sign: $r = \dfrac{-9t + 24t + 20}{6t + 5}$ $r = \dfrac{15t + 20}{6t + 5}$